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Syllabus for

Academic year
MVE170 - Basic stochastic processes
Grundläggande stokastiska processer
 
Syllabus adopted 2019-02-22 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Course round 1


Teaching language: English
Application code: 20128
Open for exchange students: Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 7,5c Grading: TH   7,5c   11 Jan 2021 pm J  

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)

Examiner:

Patrik Albin

  Go to Course Homepage


Course round 2

 
Teaching language: English
Application code: 99221
Open for exchange students: No
Maximum participants: 20
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 7,5c Grading: TH   7,5c    

Examiner:

Patrik Albin


  Go to Course Homepage


Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Probability theory from a first course in mathematical statistics.
Some experience of computer programming such as, for example, basic knowledge of Matlab programming.
Mathematics corresponding to what students from quite math oriented educations such as TM (Technical Mathematics) or F (Engineering Physics) learn during their first year of studies.

Aim

Give a thorough introduction and oversight of the different kind of stochastic processes that are of the greatest importance
in both applications in technical sciences and natural sciences as well as in further mathematical and mathematical statistical theory development.

Learning outcomes (after completion of the course the student should be able to)

Perform basic calculations of continuous time and discrete time Fourier transforms and inverse transforms as well as basic understanding of their usage in probability theory (that is, characteristic functions) as well as in the context of stationary random processes and linear time invariant systems (that is, spectral analysis).

Describe how continuous time and discrete time Markov chains (including queueing systems) work from a principal theoretical point of view and by means of implementation of corresponding computer code (or so called pseudo code) as well as performing computational examples on these objects. 

Describe the importance of dependence and independence between different stochastic process values (random variables) from a principal theoretical point of view as well as performing corresponding computational examples. 

Describe the basic defining properties of stationary processes, wide (weak) sense stationary processes, Gaussian processes and martingales from a principal theoretical point of view as well as performing corresponding computational examples.

Content

Introduction to Fourier transforms (characteristic functions), convolutions and Dirac’s delta-function together with a review of some important concepts from multivariate probability theory. Definition of discrete time and continuous time stochastic processes together with their finite dimensional distributions, mean functions, correlation functions and covariance functions. Processes with independent stationary increments (Levy processes) and Gaussian processes (normal processes). A quite substantial treatment of discrete time and continuous time Markov chains including applications to queueing systems (that adds up to upwards half of the total course material). Discrete time and continuous time martingales. Continuity and differentiability of stochastic processes together with integration and summation of them. Spectral densities together with white noise in continuous and discrete time. Stochastic processes as inputs to and outputs from linear time invariant systems. Computer implementation of the majority of the above mentioned classes of stochastic processes.



Organisation

Lectures and tutorials.

Literature

Hwei Hsu: Probability, Random Variables, and Random
Processes, 2nd Edition. Schaum's Outlines, McGraw-Hill 2010.

Geoffrey Grimmett och David Stirzaker: Probability and Random Processes, 3rd Edition. Oxford 2001.

Examination including compulsory elements

Written exam.


Published: Mon 28 Nov 2016.